PRP Records

Probable Primes Top 10000

(190562 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
90012^175801+1155*17580152922Henri Lifchitz01/2005
900211^50801-909052904Enzo Doria02/2013
900343^32374+1252882Robert Price11/2013
90042^175628+1352870Lelio R Paula01/2011
90052^175615-174752866Yves Minet09/2012
9006(13*10^52861+107)/352862Robert Price11/2017
90079*2^175586-752858Lelio R Paula03/2014
900812174^12937+12937^1217452854Norbert Schneider04/2016
9009(15*2^175565+1)/835952848Lelio R Paula07/2012
9010(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
901114256^5077+5077^1425652828Hans Havermann06/2016
90122^175467+8287552821Lelio R Paula07/2012
9013(7*10^52819+167)/352820Robert Kinser10/2017
9014(67607*2^175426+1)/352813Lelio R Paula05/2014
901513^47400-6052801Lelio R Paula01/2013
90164*10^52792+6352793Robert Price06/2016
9018(78557*2^175360+1)/308752791Lelio R Paula06/2014
901718^42055-292952791Enzo Doria03/2013
90199*5^75521+252788Lelio R Paula09/2014
90206^67814+3152770Lelio R Paula10/2012
902170^28600+6952770Norbert Schneider10/2012
902214^46038+9752766Lelio R Paula01/2013
9023(61*10^52763-7)/952764Serge Batalov02/2009
90242*5^75474+952755Lelio R Paula09/2014
902510^52753+282643060952754Robert Price05/2015
902610^52753+18399752754Patrick De Geest01/2016
902710^52753-5015352753Patrick De Geest03/2016
902819846^455+455^1984652751Anatoly F. Selevich02/2007
90292^175217+7297752746Enzo Doria04/2016
9030p(11466)#/2-25652746Robert Price05/2017
9031(4*10^52740+41)/952740Robert Price11/2014
90322^175189+538552738Lelio R Paula08/2009
90332^175160+938552729Lelio R Paula07/2008
903412356^12885+12885^1235652724Norbert Schneider03/2016
90352^175137+1152722Lelio R Paula01/2011
903665^29077-64^2907752715Robert Price08/2013
90372*10^52713-8752714Robert Price06/2016
90382^175106-46552713Lelio R Paula08/2009
90392^175089-5869552708Lelio R Paula08/2009
90402^175045+19552694Lelio R Paula02/2011
9041195^23010-252694Lelio R Paula10/2017
90422^175025+14952688Lelio R Paula02/2011
9044(19^41201+1)/2052685Paul Bourdelais03/2010
9043(436*10^52683-13)/952685Robert Price10/2017
90452*12^48815-5^4881552681Mike Oakes10/2010
9046335^20862-20862^33552678Norbert Schneider09/2015
90472^174983-760552676Lelio R Paula07/2009
90484*10^52667+1952668Robert Price04/2016
9049(10^52667+77)/352667Robert Price01/2017
905011434^12977+12977^1143452664Norbert Schneider04/2016
90512^174941-120352663Lelio R Paula07/2009
90522^174910+1270552654Lelio R Paula07/2012
90533^110338+7452645Lelio R Paula10/2012
90545^75303+1252635Lelio R Paula10/2012
90552^174836+25525552631Lelio R Paula07/2009
9056(66^28921+1)/6752622Paul Bourdelais08/2017
905720^40443+952618Lelio R Paula01/2013
9058(11*2^174788+1)/952617Lelio R Paula01/2012
9059(11*2^174786-1)/70352615Lelio R Paula01/2014
906011^50520-129052612Enzo Doria11/2012
9061(10^52608-19)/952608Robert Price10/2017
9062(9913*2^174736-1)/33352603Lelio R Paula03/2015
906313145^10024+10024^1314552594Hans Havermann05/2016
90645003^14217-15052592Enzo Doria07/2012
906519^41123+1052587Lelio R Paula01/2013
90662^174683+1290952585Lelio R Paula01/2011
90672^174643+5952573Lelio R Paula01/2011
9068(1017*2^174640-1)/77352572Lelio R Paula03/2015
906913529^7662+7662^1352952552Hans Havermann06/2016
9070121421#+18876752548Makoto Morimoto02/2016
907120^40375-592352530Enzo Doria03/2013
9072(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9073(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
90742^174462+34552519Lelio R Paula07/2009
9075t(178863)52509Robert Price10/2014
90762^174416+85552505Lelio R Paula07/2009
90776^67467-10352500Lelio R Paula10/2012
9078(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
90792^174329-1126552479Enzo Doria06/2014
90802^174314-124152474Yves Minet05/2009
908152^30577-5152471Norbert Schneider08/2014
908215692^2205+2205^1569252465Hans Havermann06/2016
9083(2^174281-7)/62881702961552453Lelio R Paula02/2012
9084(2^174240+5)/352451Lelio R Paula02/2012
9085(86*10^52450-221)/952451Robert Price06/2017
9086(62*10^52448-197)/952449Robert Price10/2017
9087(15*2^174221+1)/40352445Lelio R Paula07/2012
908826313!2-3252443Robert Price10/2015
9089(3*2^174214-1)/374872952438Lelio R Paula01/2014
90902*3^109900-552436Lelio R Paula03/2014
90924159^14488-15052432Enzo Doria07/2012
9091(89*10^52431-71)/952432Robert Price11/2015
90932^174170-394152431Yves Minet04/2017
9094(7*2^174171-1)/68552429Lelio R Paula01/2014
9096(260137^9679+1)/26013852409Faysal YAtim03/2008
90952^174098+7952409Lelio R Paula01/2011
909735^33940-221452406Enzo Doria03/2013
909815^44557+252404Ray Chandler07/2011
90992^174049-43952394Yves Minet01/2012
91006^67329+11552393Lelio R Paula10/2012
91022^174041+26214552392Lelio R Paula07/2009
9101141^24377+252392Lelio R Paula05/2013
9103lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
91042^174001-595552380Lelio R Paula07/2009
9105lucasV(-1,2,347969)52375Mike Oakes02/2017
91063^109764-14052371Lelio R Paula10/2012
91072*3^109761+752370Lelio R Paula03/2014
91089863^13112-13112^986352370Norbert Schneider10/2017
91092^173944-11225352363Enzo Doria06/2014
91112^173940+111152362Lelio R Paula01/2011
9110(3126^14983-1)/312552362Richard Fischer03/2015
911215214^2763+2763^1521452358Hans Havermann05/2016
911313200^9247+9247^1320052352Hans Havermann05/2016
9114(1017*2^173867-1)/717552339Lelio R Paula03/2015
911513732^6465+6465^1373252327Hans Havermann05/2016
9116(2^173867-1)/5253663750268952326Donovan Johnson06/2005
91172^173811-68487752323Paul Bourdelais11/2012
91182^173807-595552322Lelio R Paula06/2009
91192^173796-104468952318Paul Bourdelais11/2012
912010^52317+6449752318Patrick De Geest12/2012
912110^52317+6474352318Patrick De Geest12/2012
912310^52317-7152317Robert Price05/2011
912210821^12968+12968^1082152317Norbert Schneider04/2016
9124(298*10^52308-7)/352310Robert Price06/2017
9125(2^173778-3)/5795952308Lelio R Paula02/2012
912610232^13043-13043^1023252302Norbert Schneider08/2017
91282^173727+952298Lelio R Paula01/2011
9127(14^45631+13^45631)/2752298Robert Price04/2013
912937856!3+656152293Robert Price11/2015
91304*3^109596+552292Lelio R Paula03/2014
913115436^2441+2441^1543652291Hans Havermann05/2016
913243^32005+2452280Robert Price11/2013
91332^173650-16552274Lelio R Paula02/2011
91344*10^52272+9352273Robert Price01/2017
913519^40873+8452267Lelio R Paula01/2013
91362^173621+424242952266Jason Earls09/2008
91379999^13064-13064^999952256Norbert Schneider09/2017
9138numbpart(46909^2-1)52247Serge Batalov04/2017
913914^45579-3152240Lelio R Paula01/2013
9140(10223*2^173518+1)/90352236Lelio R Paula05/2014
914120^40147-612352233Enzo Doria03/2013
91424^86754-3^(86754+1)52232Robert Price04/2016
91432^173477-343352222Yves Minet04/2009
9144(22*10^52217-73)/352218Robert Price09/2017
9145(25*2^173446+1)/6152213Lelio R Paula07/2012
91463^109431-3852212Lelio R Paula10/2012
91472^173424-395952206Yves Minet04/2017
914813^46861-7252201Lelio R Paula01/2013
91492^173373-136352191Yves Minet03/2009
915011^50114-174052189Enzo Doria11/2012
915113735^6304+6304^1373552188Hans Havermann05/2016
915211^50111-111052186Enzo Doria11/2012
9153lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
915420^40105-858352178Enzo Doria03/2013
9155(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
91562^173314-394152173Yves Minet04/2017
91572^173294+115552167Lelio R Paula07/2012
9158(19*2^173301-1)/2348952166Lelio R Paula01/2014
915915146^2781+2781^1514652166Hans Havermann06/2016
916011^50088-3252162Lelio R Paula01/2013
91613^109320+23652159Lelio R Paula10/2012
91622^173246-2863552153Lelio R Paula06/2009
91632*10^52147+1152148Robert Price01/2015
91642^173208-11262552141Enzo Doria06/2014
9165(9179*2^173206-1)/203552141Lelio R Paula03/2015
916615^44333-7652140Lelio R Paula01/2013
91672^173187-318952135Yves Minet10/2014
91682^173167+7557952129Enzo Doria04/2016
9169(2^173169+7)/9279352125Lelio R Paula02/2012
9170(25*10^52119+23)/352120Robert Price06/2017
91719*7^61671+452119Lelio R Paula09/2014
91732^173130-922152118Lelio R Paula07/2008
9172(17*2^173129-1)/352118Lelio R Paula01/2014
91742^173100-11255952109Enzo Doria06/2014
91752^173091-11233952106Enzo Doria06/2014
917611^50030+2852101Lelio R Paula01/2013
9177(59*10^52099+13)/952100Robert Price09/2015
91782^173064-182952098Yves Minet09/2012
91792^173062-136152097Yves Minet08/2012
91803^109190-7052097Lelio R Paula10/2012
91812^173059+9019552096Lelio R Paula07/2012
91822^173048-11262552093Enzo Doria06/2014
918392^26524+9152088Norbert Schneider04/2013
918441^32295-4052085Theodore Burton02/2007
91852^173002+17752079Lelio R Paula02/2011
9186p(11334)#/2+852075Robert Price01/2017
91872^172965-11236352068Enzo Doria06/2014
91889*2^172935+752060Lelio R Paula03/2014
918911^49978-819052047Enzo Doria02/2013
919010^52041+63352042Patrick De Geest11/2012
919110^52041-9352041Robert Price05/2011
9192(21*2^172815-1)/86952021Lelio R Paula01/2014
9193(182*10^52018+1)/352020Robert Price02/2017
91944*6^66843-552015Lelio R Paula09/2014
919519^40670-5452007Lelio R Paula01/2013
91962^172756-11288352005Enzo Doria06/2014
919711832^12763-12763^1183251985Norbert Schneider02/2017
91987^61511-3651983Lelio R Paula10/2012
919910591^12914-12914^1059151979Norbert Schneider05/2017
92002^172640-7551970Lelio R Paula01/2011
9201gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
920212240^12709-12709^1224051952Norbert Schneider01/2017
9203t(173589)51951Robert Price12/2014
92047^61469+3451948Lelio R Paula10/2012
92059*2^172553-751945Lelio R Paula03/2014
920611542^12787+12787^1154251945Norbert Schneider01/2016
920735^33640-708651943Enzo Doria03/2013
9208(7*2^172534+1)/247951936Lelio R Paula07/2012
9209(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9210(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9211((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9212((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9213((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9214((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
92162^172470+751919Lelio R Paula01/2011
9215((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9217((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9218((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9219((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9220((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
92232^172455+1551915Lelio R Paula01/2011
9221((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9222((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9224((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9225((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9226((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9227((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9228((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9229((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
92305^74263+5451908Lelio R Paula10/2012
923113804^5755+5755^1380451904Hans Havermann05/2016
92327*2^172403-351900Henri Lifchitz06/2003
9233t(196078)51892Robert Price02/2014
92342*3^108759-751892Lelio R Paula03/2014
9235(94*10^51889+11)/351891Robert Price02/2017
9236(73*10^51889+17)/951890Robert Price10/2015
923735^33603-402651886Enzo Doria03/2013
92382^172350-10751883Lelio R Paula02/2011
923914419^3960+3960^1441951876Hans Havermann05/2016
92402^172325-11318551875Enzo Doria07/2014
924110^51872+10068351873Patrick De Geest06/2016
924210^51872-100000000151872Robert Price05/2016
924310^51872-10014951872Patrick De Geest06/2016
92442147092^8192+6351871Jens K. Andersen04/2009
924513^46564-2451870Lelio R Paula01/2013
924610524^12893-12893^1052451858Norbert Schneider05/2017
924713981^5110+5110^1398151848Hans Havermann05/2016
92482^172228+7626151846Enzo Doria04/2016
924911^49772-126051833Enzo Doria11/2012
9250(11*2^172157-1)/35151823Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 17 2017 23:50 (Time in France)

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